Solve the problem.
-The manager of a CD store has found that if the price of a CD is $p(x)=90-\frac{x}{8}$, then $x C D$ will be sold. Find an expression for the total revenue from the sale of $x$ CDs
(hint: revenue $=$ demand $\times$ price). Use your expression to determine the maximum revenue.
A) $\$ 32,400$
B) $\$ 8100$
C) $\$ 64,800$
D) $\$ 16,200$

Question

Quizplus · Accepted Answer

The revenue function is $R(x) = x \cdot p(x) = x \cdot (90 - \frac{x}{8}) = 90x - \frac{x^2}{8}$. To find the maximum revenue, take the derivative $R'(x) = 90 - \frac{x}{4}$, set it to zero, and solve for $x$. This gives $x = 360$. Substitute back into the revenue function: $R(360) = 90(360) - \frac{360^2}{8} = 16,200$.

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Solve the Problem $p(x)=90-\frac{x}{8}$ , Then $x C D$ Will Be Sold $x$